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# PID Controller (2 DOF), Discrete PID Controller (2 DOF)

Simulate continuous- or discrete-time two-degree-of-freedom PID controllers

## Library

Continuous, Discrete

## Description

Implement a continuous- or discrete-time two-degree-of-freedom controller (PID, PI, or PD) in your Simulink® model. The PID Controller (2DOF) block allows you to implement setpoint weighting in your controller to achieve both smooth setpoint tracking and good disturbance rejection.

The PID Controller (2DOF) block generates an output signal based on the difference between a reference signal and a measured system output. The block computes a weighted difference signal for each of the proportional, integral, and derivative actions according to the setpoint weights you specify. The block output is the sum of the proportional, integral, and derivative actions on the respective difference signals, where each action is weighted according to the gain parameters. A first-order pole filters the derivative action. Controller gains are tunable either manually or automatically. Automatic tuning requires Simulink Control Design™ software (PID Tuner or SISO Design Tool).

Configurable options in the PID Controller (2DOF) block include:

• Controller type (PID, PI, or PD)

• Controller form (Parallel or Ideal)

• Time domain (continuous or discrete)

• Initial conditions and reset trigger

• Output saturation limits and built-in anti-windup mechanism

• Signal tracking for bumpless control transfer and multiloop control

In one common implementation, the PID Controller (2DOF) block operates in the feedforward path of the feedback loop. The block receives a reference signal at the Ref input and a measured system output at the other input. For example:

For a single-input block that accepts an error signal (a difference between a setpoint and a system output), see the PID Controller block reference page.

You can generate code to implement your controller using any Simulink data type, including fixed-point data types. (Code generation requires Simulink Coder™ software; fixed-point implementation requires the Fixed-Point Designer™ product.)

For an example illustrating an application of the PID Controller (2 DOF) block, see the Simulink example Two Degree-of-Freedom PID Control for Setpoint TrackingTwo Degree-of-Freedom PID Control for Setpoint Tracking.

## Data Type Support

The PID Controller (2DOF) block accepts real signals of any numeric data type that Simulink software supports, including fixed-point data types. See Data Types Supported by Simulink in the Simulink documentation for more information.

## Parameters

The following table summarizes the PID Controller (2DOF)block parameters, accessible via the block parameter dialog box.

Choose controller form and type.
Choose discrete or continuous time.
Choose an integration method (discrete time).
Set and tune controller gains.
Set integrator and filter initial conditions.
Limit block output.
Configure anti-windup mechanism (when you limit block output).
Enable signal tracking.
Configure data types.
Configure block for code generation.

### Controller form

Select the controller form.

#### Settings

Parallel (Default)

Selects a controller form in which the proportional, integral, and derivative gains P, I, and D operate independently. The filter coefficient N sets the location of the pole in the derivative filter.

Parallel two-degree-of-freedom PID controller, where input 1 receives a reference signal and input 2 receives feedback from the measured system output:

The parallel two-degree-of-freedom PID controller can be equivalently modeled by the following block diagram:

R(s) represents the reference signal and Y(s) represents the feedback from measured system output. In this model, C(s) is a single degree-of-freedom controller, and F(s) acts as a prefilter on the reference signal. For a parallel two-degree-of-freedom PID controller in the Continuous-time Time-domain, the transfer functions F(s) and C(s) are:

$\begin{array}{l}{F}_{par}\left(s\right)=\frac{\left(bP+cDN\right){s}^{2}+\left(bPN+I\right)s+IN}{\left(P+DN\right){s}^{2}+\left(PN+I\right)s+IN}\\ {C}_{par}\left(s\right)=\frac{\left(P+DN\right){s}^{2}+\left(PN+I\right)s+IN}{s\left(s+N\right)}\end{array}$

where b and c are the Setpoint weight parameters.

Alternatively, the parallel two-degree-of-freedom PID controller can be modeled by the following block diagram:

R(s), Y(s), and C(s) are as discussed previously. In this realization, Q(s) acts as feed-forward conditioning on the reference signal R(s). For a parallel PID controller in the Continuous-time Time-domain, the transfer function Q(s) is:

${Q}_{par}\left(s\right)=\frac{\left(\left(b-1\right)P+\left(c-1\right)DN\right)s+\left(b-1\right)PN}{s+N}$

Ideal

Selects a controller form in which the proportional gain P acts on the sum of all actions.

Ideal two-degree-of-freedom PID controller, where input 1 receives a reference signal and input 2 receives feedback from the measured system output:

Similarly to the parallel controller form discussed previously, the ideal two-degree-of-freedom PID controller can be modeled as a single degree-of-freedom controller C(s) with a prefilter F(s). For an ideal two-degree-of-freedom PID controller in the Continuous-time Time-domain, the transfer functions F(s) and C(s) are:

$\begin{array}{l}{F}_{id}\left(s\right)=\frac{\left(b+cDN\right){s}^{2}+\left(bN+I\right)s+IN}{\left(1+DN\right){s}^{2}+\left(N+I\right)s+IN}\\ {C}_{id}\left(s\right)=P\frac{\left(1+DN\right){s}^{2}+\left(N+I\right)s+IN}{s\left(s+N\right)}\end{array}$

where b and c are the Setpoint weight parameters.

Alternatively, modeling the ideal two-degree-of-freedom PID controller as a one-degree-of-freedom controller C(s) with feed-forward conditioning Q(s) on the reference signal gives, in continuous-time:

${Q}_{id}\left(s\right)=P\frac{\left(\left(b-1\right)+\left(c-1\right)DN\right)s+\left(b-1\right)N}{s+N}$

The controller transfer function for the current settings is displayed in the block dialog box.

### Controller

Specify the controller type.

#### Settings

PID (Default)

Implements a controller with proportional, integral, and derivative action.

PI

Implements a controller with proportional and integral action.

PD

Implements a controller with proportional and derivative action.

The controller transfer function for the current settings is displayed in the block dialog box.

### Time-domain

Select continuous or discrete time domain. The appearance of the block changes to reflect your selection.

#### Settings

Continuous-time (Default)

Selects the continuous-time representation.

Discrete-time

Selects the discrete-time representation. Selecting Discrete-time also allows you to specify the:

• Sample time, which is the discrete interval between samples.

• Discrete integration methods for the integrator and the derivative filter using the Integrator method and Filter method menus.

### Integrator method

(Available only when you set Time-domain to Discrete-time.) Specify the method used to compute the integrator output. For more information about discrete-time integration methods, see the Discrete-Time Integrator block reference page.

#### Settings

Forward Euler (Default)

Selects the Forward Rectangular (left-hand) approximation.

This method is best for small sampling times, where the Nyquist limit is large compared to the bandwidth of the controller. For larger sampling times, the Forward Euler method can result in instability, even when discretizing a system that is stable in continuous time.

Backward Euler

Selects the Backward Rectangular (right-hand) approximation.

An advantage of the Backward Euler method is that discretizing a stable continuous-time system using this method always yields a stable discrete-time result.

If you activate the Back-calculation Anti-windup method, this integration method can cause algebraic loops in your controller. Algebraic loops can slow down simulation of the model. In addition, if you want to generate code using Simulink Coder software or the Fixed-Point Designer product, you cannot generate code for a model that contains an algebraic loop. For more information about algebraic loops in Simulink models, see Algebraic Loops in the Simulink documentation.

Trapezoidal

Selects the Bilinear approximation.

An advantage of the Trapezoidal method is that discretizing a stable continuous-time system using this method always yields a stable discrete-time result. Of all available integration methods, the Trapezoidal method yields the closest match between frequency-domain properties of the discretized system and the corresponding continuous-time system.

If you activate the Back-calculation Anti-windup method, this integration method can cause algebraic loops in your controller. Algebraic loops can slow down simulation of the model. In addition, if you want to generate code using Simulink Coder software or the Fixed-Point Designer product, you cannot generate code for a model that contains an algebraic loop. For more information about algebraic loops in Simulink models, see Algebraic Loops in the Simulink documentation.

### Filter method

(Available only when you set Time-domain to Discrete-time.) Specify the method used to compute the derivative filter output. For more information about discrete-time integration methods, see the Discrete-Time Integrator block reference page.

#### Settings

Forward Euler (Default)

Selects the Forward Rectangular (left-hand) approximation.

This method is best for small sampling times, where the Nyquist limit is large compared to the bandwidth of the controller. For larger sampling times, the Forward Euler method can result in instability, even when discretizing a system that is stable in continuous time.

Backward Euler

Selects the Backward Rectangular (right-hand) approximation.

An advantage of the Backward Euler method is that discretizing a stable continuous-time system using this method always yields a stable discrete-time result. Any filter parameter value N > 0 yields a stable result with this method.

This filter method can cause algebraic loops in your controller. Algebraic loops can slow down simulation of the model. In addition, if you want to generate code using Simulink Coder software or the Fixed-Point Designer product, you cannot generate code for a model that contains an algebraic loop. For more information about algebraic loops in Simulink models, see Algebraic Loops in the Simulink documentation.

Trapezoidal

Selects the Bilinear approximation.

An advantage of the Trapezoidal method is that discretizing a stable continuous-time system using this method always yields a stable discrete-time result. Any filter parameter value N > 0 yields a stable result with this method. Of all available filter methods, the Trapezoidal method yields the closest match between frequency-domain properties of the discretized system and the corresponding continuous-time system.

This filter method can cause algebraic loops in your controller. Algebraic loops can slow down simulation of the model. In addition, if you want to generate code using Simulink Coder software or the Fixed-Point Designer product, you cannot generate code for a model that contains an algebraic loop. For more information about algebraic loops in Simulink models, see Algebraic Loops in the Simulink documentation.

### Sample time (-1 for inherited)

(Available only when you set Time-domain to Discrete-time.) Specify the discrete interval between samples.

#### Settings

Default: 1

By default, the block uses a discrete sample time of 1. To specify a different sample time, enter another discrete value, such as 0.1.

If you specify a value of –1, the PID Controller (2DOF) block inherits the sample time from upstream blocks. Do not enter a value of 0; to implement a continuous-time controller, select the Time-domain Continuous-time.

### Proportional (P)

Specify the proportional gain P.

Default: 1

Enter a finite, real gain value into the Proportional (P) field. Use either scalar or vector gain values. For a parallel PID Controller form, the proportional action is independent of the integral and derivative actions. For an ideal PID Controller form, the proportional action acts on the integral and derivative actions. See Controller form for more information about the role of P in the controller transfer function.

When you have Simulink Control Design software installed, you can automatically tune the controller gains using the PID Tuner or the SISO Design Tool. See Choosing a Control Design Approach.

### Integral (I)

(Available for PID and PI controllers.) Specify the integral gain I.

Default: 1

Enter a finite, real gain value into the Integral (I) field. Use either scalar or vector gain values.

When you have Simulink Control Design software installed, you can automatically tune the controller gains using the PID Tuner or the SISO Design Tool. See Choosing a Control Design Approach.

### Derivative (D)

(Available for PID and PD controllers.) Specify the derivative gain D.

Default: 0

Enter a finite, real gain value into the Derivative (D) field. Use either scalar or vector gain values.

When you have Simulink Control Design software installed, you can automatically tune the controller gains using the PID Tuner or the SISO Design Tool. See Choosing a Control Design Approach.

### Filter coefficient (N)

Specifies the filter coefficient of the controller.

(Available for PID and PD controllers, when Use filtered derivative is checked.) Specify the filter coefficient N, which determines the pole location of the filter in the derivative action:

The filter pole falls at s = -N in the Continuous-time Time-domain. For Discrete-time, the location of the pole depends on which Filter method you select (for sampling time Ts):

• Forward Euler:

${z}_{pole}=1-N{T}_{s}$

• Backward Euler:

${z}_{pole}=\frac{1}{1+N{T}_{s}}$

• Trapezoidal:

${z}_{pole}=\frac{1-N{T}_{s}/2}{1+N{T}_{s}/2}$

Default: 100.

Enter a finite, real gain value into the Filter Coefficient (N) field. Use either scalar or vector gain values. Note that the PID controller (2DOF) block does not support N = inf (ideal unfiltered derivative).

When you have Simulink Control Design software installed, you can automatically tune the controller gains using the PID Tuner or the SISO Design Tool. See Choosing a Control Design Approach. Automatic tuning requires N > 0.

### Use Filtered Derivative

Specify whether derivative term is filtered (finite N) or unfiltered. Unfiltered derivative is available only for discrete-time controllers.

Unchecking this option replaces the filtered derivative with a discrete differentiator. For example, if Filter Method is Forward Euler, then the filtered derivative term is represented by:

When you uncheck Use filtered derivative, the derivative term becomes:

#### Settings

On (Default)

Use derivative filter (finite N).

Off

Derivative is unfiltered.

### Setpoint weight (b)

Specify the proportional setpoint weight b.

Default: 1

Enter the proportional setpoint weight value into the Setpoint weight (b) field. Setting b = 0 eliminates the proportional action on the reference signal, which can reduce overshoot in the system response to step changes in the setpoint.

The following diagrams show the role of Setpoint weight (b) in Parallel and Ideal PID controllers. See Controller form for a discussion of the corresponding transfer functions.

Parallel Two-Degree-of-Freedom PID Controller

Ideal Two-Degree-of-Freedom PID Controller

### Setpoint weight (c)

(Available for PID and PD controllers.) Specify the derivative setpoint weight c.

Enter the derivative setpoint weight value into the Setpoint weight (c) field. To implement a controller that achieves both effective disturbance rejection and smooth setpoint tracking without excessive transient response, set c = 0. Setting c = 0 yields a controller with derivative action on the measured system response but not on the reference input.

The following diagrams show the role of Setpoint weight (c) in Parallel and Ideal PID controllers. See Controller form for a discussion of the corresponding transfer functions.

Parallel Two-Degree-of-Freedom PID Controller

Ideal Two-Degree-of-Freedom PID Controller

### Initial conditions Source

Select the source of the integrator and filter initial conditions. Simulink uses initial conditions to initialize the integrator and filter output at the start of a simulation or at a specified trigger event (see External reset). The integrator and filter initial conditions in turn determine the initial block output.

#### Settings

internal (Default)

Specifies the integrator and filter initial conditions explicitly using the Integrator Initial condition and Filter Initial condition parameters.

external

Specifies the integrator and filter initial conditions externally. An additional input port appears under the block inputs for each initial condition: I0 for the integrator and D0 for the filter:

### Integrator Initial condition

(Available only when Initial conditions Source is internal and the controller includes integral action.) Specify the integrator initial value. Simulink uses the initial condition to initialize the integrator output at the start of a simulation or at a specified trigger event (see External reset). The integrator initial condition, together with the filter initial condition, determines the initial output of the PID Controller (2DOF) block.

Default: 0

Simulink does not permit the integrator initial condition to be inf or NaN.

### Filter Initial condition

(Available only when Initial conditions Source is internal, the controller includes derivative action, and Use filtered derivative is checked.) Specify the filter initial value. Simulink uses the initial condition to initialize the filter output at the start of a simulation or at a specified trigger event (see External reset). The filter initial condition, together with the integrator initial condition, determines the initial output of the PID Controller (2DOF) block.

Default: 0

Simulink does not permit the filter initial condition to be inf or NaN.

### External reset

Select the trigger event that resets the integrator and filter outputs to the initial conditions you specify in the Integrator Initial condition and Filter Initial condition fields. Selecting any option other than none enables a reset input on the block for the external reset signal, as shown:

Or, if the Initial conditions Source is External:

The reset signal must be a scalar of type single, double, boolean, or integer. Fixed point data types, except for ufix1, are not supported.

 Note:   To be compliant with the Motor Industry Software Reliability Association (MISRA®) software standard, your model must use Boolean signals to drive the external reset ports of the PID controller (2DOF) block.

#### Settings

none (Default)

Does not reset the integrator and filter outputs to initial conditions.

rising

Resets the outputs when the reset signal has a rising edge.

falling

Resets the outputs when the reset signal has a falling edge.

either

Resets the outputs when the reset signal either rises or falls.

level

Resets and holds the outputs to the initial conditions while the reset signal is nonzero.

### Ignore reset when linearizing

Force Simulink linearization commands to ignore any reset mechanism that you have chosen with the External reset menu. Ignoring reset states allows you to linearize a model around an operating point even if that operating point causes the PID Controller (2DOF) block to reset.

#### Settings

Off (Default)

Simulink linearization commands do not ignore states corresponding to the reset mechanism.

On

Simulink linearization commands ignore states corresponding to the reset mechanism.

### Enable zero-crossing detection

Enable zero-crossing detection in continuous-time models upon reset and upon entering or leaving a saturation state.

Zero-crossing detection can accurately locate signal discontinuities without resorting to excessively small time steps that can lead to lengthy simulation times. If you select Limit output or activate an External reset in your PID Controller (2DOF) block, activating zero-crossing detection can reduce computation time in your simulation. For more information, see Zero-Crossing Detection.

#### Settings

On (Default)

Uses zero-crossing detection at any of the following events: reset; entering or leaving an upper saturation state; and entering or leaving a lower saturation state.

Off

Does not use zero-crossing detection.

Enabling zero-crossing detection for the PID Controller (2DOF) block also enables zero-crossing detection for all under-mask blocks that include the zero-crossing detection feature.

### Limit output

Limit the block output to values you specify as the Lower saturation limit and Upper saturation limit parameters.

Activating this option limits the block output internally to the block, obviating the need for a separate Saturation block after the controller in your Simulink model. It also allows you to activate the built-in anti-windup mechanism (see Anti-windup method).

#### Settings

Off (Default)

Does not limit the block output, which is the weighted sum of the proportional, integral, and derivative actions.

On

Limits the block output to the Lower saturation limit or the Upper saturation limit whenever the weighted sum exceeds those limits. Allows you to select an Anti-windup method.

### Lower saturation limit

(Available only when you select the Limit Output box.) Specify the lower limit for the block output. The block output is held at the Lower saturation limit whenever the weighted sum of the proportional, integral, and derivative actions goes below that value.

Default: -inf

### Upper saturation limit

(Available only when you select the Limit Output box.) Specify the upper limit for the block output. The block output is held at the Upper saturation limit whenever the weighted sum of the proportional, integral, and derivative actions exceeds that value.

Default: inf

### Anti-windup method

(Available only when you select the Limit Output option and the controller includes integral action.) Select an anti-windup mechanism to discharge the integrator when the block is saturated, which occurs when the sum of the block components exceeds the output limits.

When you select the Limit output check box and the weighted sum of the controller components exceeds the specified output limits, the block output holds at the specified limit. However, the integrator output can continue to grow (integrator wind-up), increasing the difference between the block output and the sum of the block components. Without a mechanism to prevent integrator wind-up, two results are possible:

• If the sign of the input signal never changes, the integrator continues to integrate until it overflows. The overflow value is the maximum or minimum value for the data type of the integrator output.

• If the sign of the input signal changes once the weighted sum has grown beyond the output limits, it can take a long time to discharge the integrator and return the weighted sum within the block saturation limit.

In both cases, controller performance can suffer. To combat the effects of wind-up without an anti-windup mechanism, it may be necessary to detune the controller (for example, by reducing the controller gains), resulting in a sluggish controller. Activating an anti-windup mechanism can improve controller performance.

#### Settings

none (Default)

Does not use an anti-windup mechanism. This setting can cause the block's internal signals to be unbounded even if the output appears to be bounded by the saturation limits. This can result in slow recovery from saturation or unexpected overflows.

back-calculation

Discharges the integrator when the block output saturates using the integral-gain feedback loop:

You can also specify a value for the Back-calculation coefficient (Kb).

clamping

Stops integration when the sum of the block components exceeds the output limits and the integrator output and block input have the same sign. Resumes integration when the sum of the block components exceeds the output limits and the integrator output and block input have opposite sign. The integrator portion of the block is:

The clamping circuit implements the logic necessary to determine whether integration continues.

### Back-calculation gain (Kb)

(Available only when the back-calculation Anti-windup method is active.) Specify the gain coefficient of the anti-windup feedback loop.

The back-calculation anti-windup method discharges the integrator on block saturation using a feedback loop having gain coefficient Kb.

Default: 1

### Ignore saturation when linearizing

Force Simulink linearization commands ignore PID Controller (2DOF) block output limits. Ignoring output limits allows you to linearize a model around an operating point even if that operating point causes the PID Controller (2DOF) block to exceed the output limits.

#### Settings

On (Default)

Simulink linearization commands ignore states corresponding to saturation.

Off

Simulink linearization commands do not ignore states corresponding to saturation.

### Enable tracking mode

(Available for any controller with integral action.) Activate signal tracking, which lets the output of the PID Controller (2DOF) block follow a tracking signal. Provide the tracking signal to the block at the TR port, which becomes active when you select Enable tracking mode.

When signal tracking is active, the difference between the tracked signal and the block output is fed back to the integrator input with a gain Kt. You can also specify the value of the Tracking coefficient (Kt).

For information about using tracking mode to implement bumpless control transfer scenarios and multiloop controllers, see Enable tracking mode in the PID Controller reference page.

#### Settings

Off (Default)

Disables signal tracking and removes TR block input.

On

Enables signal tracking and activates TR input.

### Tracking gain (Kt)

(Available only when you select Enable tracking mode.) Specify Kt, which is the gain of the signal tracking feedback loop.

Default: 1

### Parameter data type

Select the data type of the gain parameters P, I, D, N, Kb, and Kt and the setpoint weighting parameters b and c.

#### Settings

Inherit: Inherit via internal rule (Default)

Simulink chooses a data type to balance numerical accuracy, performance, and generated code size, while taking into account the properties of the embedded target hardware. If you change the embedded target settings, the data type selected by the internal rule might change. It is not always possible for the software to optimize code efficiency and numerical accuracy at the same time. If the internal rule doesn't meet your specific needs for numerical accuracy or performance, use one of the following options:

• Specify the output data type explicitly.

• Use the simple choice of Inherit: Same as input.

• Explicitly specify a default data type such as fixdt(1,32,16) and then use the Fixed-Point Tool to propose data types for your model. For more information, see fxptdlg.

• To specify your own inheritance rule, use Inherit: Inherit via back propagation and then use a Data Type Propagation block. Examples of how to use this block are available in the Signal Attributes library Data Type Propagation Examples block.

Inherit: Inherit via back propagation

Use data type of the driving block.

Inherit: Same as input

Use data type of input signal.

double

single

int8

uint8

int16

uint16

int32

uint32

fixdt(1,16)

fixdt(1,16,0)

fixdt(1,16,2^0,0)

<data type expression>

Name of a data type object. For example, Simulink.NumericType.

### Product output data type

Select the product output data type of the gain parameters P, I, D, N, Kb, and Kt and the setpoint weighting parameters b and c .

#### Settings

Inherit: Inherit via internal rule (Default)

Simulink chooses a data type to balance numerical accuracy, performance, and generated code size, while taking into account the properties of the embedded target hardware. If you change the embedded target settings, the data type selected by the internal rule might change. It is not always possible for the software to optimize code efficiency and numerical accuracy at the same time. If the internal rule doesn't meet your specific needs for numerical accuracy or performance, use one of the following options:

• Specify the output data type explicitly.

• Use the simple choice of Inherit: Same as input.

• Explicitly specify a default data type such as fixdt(1,32,16) and then use the Fixed-Point Tool to propose data types for your model. For more information, see fxptdlg.

• To specify your own inheritance rule, use Inherit: Inherit via back propagation and then use a Data Type Propagation block. Examples of how to use this block are available in the Signal Attributes library Data Type Propagation Examples block.

Inherit: Inherit via back propagation

Use data type of the driving block.

Inherit: Same as input

Use data type of input signal.

double

single

int8

uint8

int16

uint16

int32

uint32

fixdt(1,16)

fixdt(1,16,0)

fixdt(1,16,2^0,0)

<data type expression>

Name of a data type object. For example, Simulink.NumericType.

### Summation output data type

Select the summation output data type of the sums Sum, Sum1, Sum2, Sum3, Sum D, Sum I1 , SumI2 ,and SumI3, which are sums computed internally within the block. To see where Simulink computes each of these sums , right-click the PID Controller (2DOF) block in your model and select Look Under Mask:

• Sum is the weighted sum of the proportional, derivative, and integral signals.

• Sum1 is the difference between the reference input weighted by b and the measured system response.

• Sum2 is the difference between the reference input weighted by c and the measured system response.

• Sum3 is the difference between the unweighted reference input and the measured system response.

• SumD is the sum in the derivative filter feedback loop.

• SumI1 is the sum of the block input signal (weighted by the integral gain I) and SumI2. SumI1 is computed only when Limit output and Anti-windup method back-calculation are active.

• SumI2 is the difference between the weighted sum Sum and the limited block output. SumI2 is computed only when Limit output and Anti-windup method back-calculation are active.

• SumI3 is the difference between the block output and the signal at the block's tracking input. SumI3 is computed only when you select the Enable tracking mode box.

#### Settings

Inherit: Inherit via internal rule (Default)

Simulink chooses a data type to balance numerical accuracy, performance, and generated code size, while taking into account the properties of the embedded target hardware. If you change the embedded target settings, the data type selected by the internal rule might change. It is not always possible for the software to optimize code efficiency and numerical accuracy at the same time. If the internal rule doesn't meet your specific needs for numerical accuracy or performance, use one of the following options:

• Specify the output data type explicitly.

• Use the simple choice of Inherit: Same as first input.

• Explicitly specify a default data type such as fixdt(1,32,16) and then use the Fixed-Point Tool to propose data types for your model. For more information, see fxptdlg.

 Note:   The accumulator internal rule favors greater numerical accuracy, possibly at the cost of less efficient generated code. To get the same accuracy for the output, set the output data type to Inherit: Same as accumulator.
Inherit: Inherit via back propagation

Use data type of the driving block.

Inherit: Same as first input

Use data type of first input signal.

Inherit: Same as accumulator

Use the same data type as the corresponding accumulator.

double

single

int8

uint8

int16

uint16

int32

uint32

fixdt(1,16)

fixdt(1,16,0)

fixdt(1,16,2^0,0)

<data type expression>

Name of a data type object. For example, Simulink.NumericType.

### Accumulator data type

Specify the accumulator data type.

#### Settings

Default: Inherit: Inherit via internal rule

Inherit: Inherit via internal rule

Use internal rule to determine accumulator data type.

Inherit: Same as first input

Use data type of first input signal.

double

Accumulator data type is double.

single

Accumulator data type is single.

int8

Accumulator data type is int8.

uint8

Accumulator data type is uint8.

int16

Accumulator data type is int16.

uint16

Accumulator data type is uint16.

int32

Accumulator data type is int32.

uint32

Accumulator data type is uint32.

fixdt(1,16,0)

Accumulator data type is fixed point fixdt(1,16,0).

fixdt(1,16,2^0,0)

Accumulator data type is fixed point fixdt(1,16,2^0,0).

<data type expression>

The name of a data type object, for example Simulink.NumericType

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Integrator output data type

Select the data type of the integrator output.

#### Settings

Inherit: Inherit via internal rule (Default)

Simulink chooses a data type to balance numerical accuracy, performance, and generated code size, while taking into account the properties of the embedded target hardware. If you change the embedded target settings, the data type selected by the internal rule might change. It is not always possible for the software to optimize code efficiency and numerical accuracy at the same time. If the internal rule doesn't meet your specific needs for numerical accuracy or performance, use one of the following options:

• Specify the output data type explicitly.

• Use Inherit: Inherit via back propagation.

• Explicitly specify a default data type such as fixdt(1,32,16) and then use the Fixed-Point Tool to propose data types for your model. For more information, see fxptdlg.

Inherit: Inherit via back propagation

Use data type of the driving block.

double

single

int8

uint8

int16

uint16

int32

uint32

fixdt(1,16)

fixdt(1,16,0)

fixdt(1,16,2^0,0)

<data type expression>

Name of a data type object. For example, Simulink.NumericType.

### Filter output data type

Select the data type of the filter output.

#### Settings

Inherit: Inherit via internal rule (Default)

Simulink chooses a data type to balance numerical accuracy, performance, and generated code size, while taking into account the properties of the embedded target hardware. If you change the embedded target settings, the data type selected by the internal rule might change. It is not always possible for the software to optimize code efficiency and numerical accuracy at the same time. If the internal rule doesn't meet your specific needs for numerical accuracy or performance, use one of the following options:

• Specify the output data type explicitly.

• Use Inherit: Inherit via back propagation.

• Explicitly specify a default data type such as fixdt(1,32,16) and then use the Fixed-Point Tool to propose data types for your model. For more information, see fxptdlg.

Inherit: Inherit via back propagation

Use data type of the driving block.

double

single

int8

uint8

int16

uint16

int32

uint32

fixdt(1,16)

fixdt(1,16,0)

fixdt(1,16,2^0,0)

<data type expression>

Name of a data type object. For example, Simulink.NumericType.

### Saturation output data type

Select the saturation output data type.

#### Settings

Inherit: Same as input (Default)

Use data type of input signal.

Inherit: Inherit via back propagation

Use data type of the driving block.

double

single

int8

uint8

int16

uint16

int32

uint32

fixdt(1,16)

fixdt(1,16,0)

fixdt(1,16,2^0,0)

<data type expression>

Name of a data type object. For example, Simulink.NumericType.

### Mode

Select the category of data to specify.

#### Settings

Default: Inherit

Inherit

Inheritance rules for data types. Selecting Inherit enables a second menu/text box to the right. Select one of the following choices:

• Inherit via internal rule (default)

• Inherit via back propagation

• Same as first input

• Same as accumulator

Built in

Built-in data types. Selecting Built in enables a second menu/text box to the right. Select one of the following choices:

• double (default)

• single

• int8

• uint8

• int16

• uint16

• int32

• uint32

Fixed point

Fixed-point data types.

Expression

Expressions that evaluate to data types. Selecting Expression enables a second menu/text box to the right, where you can enter the expression.

#### Dependency

Clicking the Show data type assistant button enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Mode

Select the category of data to specify.

#### Settings

Default: Inherit

Inherit

Inheritance rules for data types. Selecting Inherit enables a second menu/text box to the right. Select one of the following choices:

• Inherit via back propagation

• Same as input (default)

Built in

Built-in data types. Selecting Built in enables a second menu/text box to the right. Select one of the following choices:

• double (default)

• single

• int8

• uint8

• int16

• uint16

• int32

• uint32

Fixed point

Fixed-point data types.

Expression

Expressions that evaluate to data types. Selecting Expression enables a second menu/text box to the right, where you can enter the expression.

#### Dependency

Clicking the Show data type assistant button enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Mode

Select the category of accumulator data to specify

#### Settings

Default: Inherit

Inherit

Specifies inheritance rules for data types. Selecting Inherit enables a list of possible values:

• Inherit via internal rule (default)

• Same as first input

Built in

Specifies built-in data types. Selecting Built in enables a list of possible values:

• double (default)

• single

• int8

• uint8

• int16

• uint16

• int32

• uint32

Fixed point

Specifies fixed-point data types.

Expression

Specifies expressions that evaluate to data types. Selecting Expression enables you to enter an expression.

#### Dependency

Clicking the Show data type assistant button for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Data type override

Specify data type override mode for this signal.

#### Settings

Default: Inherit

Inherit

Inherits the data type override setting from its context, that is, from the block, Simulink.Signal object or Stateflow® chart in Simulink that is using the signal.

Off

Ignores the data type override setting of its context and uses the fixed-point data type specified for the signal.

#### Tip

The ability to turn off data type override for an individual data type provides greater control over the data types in your model when you apply data type override. For example, you can use this option to ensure that data types meet the requirements of downstream blocks regardless of the data type override setting.

#### Dependency

This parameter appears only when the Mode is Built in or Fixed point.

### Signedness

Specify whether you want the fixed-point data as signed or unsigned.

#### Settings

Default: Signed

Signed

Specify the fixed-point data as signed.

Unsigned

Specify the fixed-point data as unsigned.

#### Dependencies

Selecting Mode > Fixed point enables this parameter.

### Signedness

Specify whether you want the fixed-point data to be signed or unsigned.

#### Settings

Default: Signed

Signed

Specify the fixed-point data to be signed.

Unsigned

Specify the fixed-point data to be unsigned.

#### Dependencies

Selecting Mode > Fixed point for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Scaling

Specify the method for scaling your fixed-point data to avoid overflow conditions and minimize quantization errors.

#### Settings

Default: Best precision, Binary point, Integer

Binary point

Specify binary point location.

Slope and bias

Enter slope and bias.

Best precision

Specify best-precision values. This option appears for some blocks.

Integer

Specify integer. This setting has the same result as specifying a binary point location and setting fraction length to 0. This option appears for some blocks.

#### Dependencies

Selecting Mode > Fixed point enables this parameter.

Selecting Binary point enables:

• Fraction length

• Calculate Best-Precision Scaling

Selecting Slope and bias enables:

• Slope

• Bias

• Calculate Best-Precision Scaling

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Scaling

Specify the method for scaling your fixed-point data to avoid overflow conditions and minimize quantization errors.

#### Settings

Default: Binary point

Binary point

Specify binary point location.

Slope and bias

Enter slope and bias.

#### Dependencies

Selecting Mode > Fixed point for the accumulator data type enables this parameter.

Selecting Binary point enables:

• Fraction length

Selecting Slope and bias enables:

• Slope

• Bias

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Word length

Specify the bit size of the word that holds the quantized integer.

Default: 16

Minimum: 0

Maximum: 32

#### Dependencies

Selecting Mode > Fixed point enables this parameter.

### Word length

Specify the bit size of the word that will hold the quantized integer.

#### Settings

Default: 16

Minimum: 0

Maximum: 32

Large word sizes represent large values with greater precision than small word sizes.

#### Dependencies

Selecting Mode > Fixed point for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Fraction length

Specify fraction length for fixed-point data type.

#### Settings

Default: 0

Binary points can be positive or negative integers.

#### Dependencies

Selecting Scaling > Binary point enables this parameter.

### Fraction length

Specify fraction length for fixed-point data type.

#### Settings

Default: 0

Binary points can be positive or negative integers.

#### Dependencies

Selecting Scaling > Binary point for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Slope

Specify slope for the fixed-point data type.

#### Settings

Default: 2^0

Specify any positive real number.

#### Dependencies

Selecting Scaling > Slope and bias enables this parameter.

### Slope

Specify slope for the fixed-point data type.

#### Settings

Default: 2^0

Specify any positive real number.

#### Dependencies

Selecting Scaling > Slope and bias for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Bias

Specify bias for the fixed-point data type.

#### Settings

Default: 0

Specify any real number.

#### Dependencies

Selecting Scaling > Slope and bias enables this parameter.

### Bias

Specify bias for the fixed-point data type.

#### Settings

Default: 0

Specify any real number.

#### Dependencies

Selecting Scaling > Slope and bias for the accumulator data type enables this parameter.

#### Command-Line Information

See Block-Specific Parameters for the command-line information.

### Lock output data type setting against changes by the fixed-point tools

Select to lock the output data type setting of this block against changes by the Fixed-Point Tool and the Fixed-Point Advisor.

#### Settings

Default: Off

On

Locks the output data type setting for this block.

Off

Allows the Fixed-Point Tool and the Fixed-Point Advisor to change the output data type setting for this block.

#### Command-Line Information

 Parameter: LockScale Type: string Value: 'off' | 'on' Default: 'off'

### Saturate on integer overflow

Specify whether overflows saturate.

#### Settings

Default: Off

On

Overflows saturate to either the minimum or maximum value that the data type can represent.

For example, an overflow associated with a signed 8-bit integer can saturate to -128 or 127.

Off

Overflows wrap to the appropriate value that is representable by the data type.

For example, the number 130 does not fit in a signed 8-bit integer and wraps to -126.

#### Tips

• Consider selecting this check box when your model has possible overflow and you want explicit saturation protection in the generated code.

• Consider clearing this check box when you want to optimize efficiency of your generated code.

Clearing this check box also helps you avoid overspecifying how a block handles out-of-range signals. For more information, see Checking for Signal Range Errors.

• When you select this check box, saturation applies to every internal operation on the block, not just the output or result.

• In general, the code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.

#### Command-Line Information

 Parameter: SaturateOnIntegerOverflow Type: string Value: 'off' | 'on' Default: 'off'

### Integer rounding mode

Specify the rounding mode for fixed-point operations.

#### Settings

Default: Floor

Ceiling

Rounds both positive and negative numbers toward positive infinity. Equivalent to the MATLAB® ceil function.

Convergent

Rounds number to the nearest representable value. If a tie occurs, rounds to the nearest even integer. Equivalent to the Fixed-Point Designer convergent function.

Floor

Rounds both positive and negative numbers toward negative infinity. Equivalent to the MATLAB floor function.

Nearest

Rounds number to the nearest representable value. If a tie occurs, rounds toward positive infinity. Equivalent to the Fixed-Point Designer nearest function.

Round

Rounds number to the nearest representable value. If a tie occurs, rounds positive numbers toward positive infinity and rounds negative numbers toward negative infinity. Equivalent to the Fixed-Point Designer round function.

Simplest

Automatically chooses between round toward floor and round toward zero to generate rounding code that is as efficient as possible.

Zero

Rounds number toward zero. Equivalent to the MATLAB fix function.

#### Command-Line Information

 Parameter: RndMeth Type: string Value: 'Ceiling' | 'Convergent' | 'Floor' | 'Nearest' | 'Round' | 'Simplest' | 'Zero' Default: 'Floor'

### State name

Assign unique name to each state. The state names apply only to the selected block.

To assign a name to a single state, enter the name between quotes; for example, 'velocity'.

To assign names to multiple states, enter a comma-delimited list surrounded by braces; for example, {'a', 'b', 'c'}. Each name must be unique. To assign state names with a variable that has been defined in the MATLAB workspace, enter the variable without quotes. The variable can be a string, cell, or structure.

#### Settings

Default: ' ' (no name)

### State name must resolve to Simulink signal object

Require that state name resolve to Simulink signal object.

#### Settings

Default: Off

On

Require that state name resolve to Simulink signal object.

Off

Do not require that state name resolve to Simulink signal object.

#### Dependencies

State name enables this parameter.

Selecting this check box disables Code generation storage class.

#### Command-Line Information

 Parameter: StateMustResolveToSignalObject Type: string Value: 'off' | 'on' Default: 'off'

### Code generation storage class

Select state storage class.

#### Settings

Default: Auto

Auto

Auto is the appropriate storage class for states that you do not need to interface to external code.

ExportedGlobal

State is stored in a global variable

ImportedExtern

model_private.h declares the state as an extern variable.

ImportedExternPointer

model_private.h declares the state as an extern pointer.

#### Dependencies

State name enables this parameter.

Setting this parameter to ExportedGlobal, ImportedExtern, or ImportedExternPointer enables Code generation storage type qualifier.

#### Command-Line Information

Command-Line Information

 Parameter: StateStorageClass Type: string Value: 'Auto' | 'ExportedGlobal' | 'ImportedExtern' | 'ImportedExternPointer' Default: 'Auto'

### Code generation storage type qualifier

Specify the Simulink Coder storage type qualifier.

#### Settings

Default: ' '

If left blank, no qualifier is assigned.

#### Dependency

Setting Code generation storage class to ExportedGlobal, ImportedExtern, or ImportedExternPointer enables this parameter.

#### Command-Line Information

 Parameter: RTWStateStorageTypeQualifier Type: string Value: ' ' Default: ' '

## Characteristics

 Direct Feedthrough The following ports support direct feedthrough:Reset portIntegrator and filter initial condition portInput port, for every integration method except Forward Euler Sample Time Specified in the Sample time parameter Scalar Expansion Supported for gain parameters P, I, and D for filter coefficient N, and for setpoint weights b and c States Inherited from driving block and parameters Dimensionalized Yes Zero-Crossing Detection Yes (in continuous-time domain)